Single-walled carbon nanotubes (SWNTs) and multi-walled nanotubes (MWNTs) are gaining appeal in mechanical engineering and industrial applications due to their direct influence on enhancing the thermal conductivity of base fluids. With such intriguing properties of carbon nanotubes in mind, our goal in this work is to investigate radiation effects on the flow of carbon nanotube suspended nanofluids in the presence of a magnetic field past a stretched sheet impacted by slip state. CNTs flow and heat transmission are frequently modelled in practice using nonlinear differential equation systems. This system has been precisely solved, and an accurate analytical expression for the fluid velocity in terms of an exponential function has been derived, while the temperature distribution is stated in terms of a confluent hypergeometric function. The impact of the radiation parameter, slip parameter, sloid volume fraction, magnetic parameter, Eckart and Prandtl numbers on the velocity, temperature, and heat transfer rate profiles are demonstrated using a parametric analysis. When compared to the two types of nanoparticles (Cooper and Silver) in earlier published articles, temperature profiles for single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs) are revealed to be particularly sensitive to radiation, solid volume fraction, and slip parameters. Nanomechanical gears, nanosensors, nanocomposite materials, resonators, and thermal materials are only a few of the present problem's technical applications.

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Due to importance of the slip effect on modeling the boundary layer flows of nanofluids, theoretical and numerical investigations have been introduced in this paper for studying the effect of a partial slip boundary condition on the heat transfer of nanofluids over a stretching sheet. The exact solutions of the investigating model were obtained in terms of exponential, Gamma, and incomplete Gamma functions at some values of the physical parameters. These solutions were then numerically validated by using Chebyshev pseudospectral differentiation matrix (ChPDM) technique. The numerical results reveal that this approach is really effective, very accurate, and convenient in studying the similar problems.

This paper elucidates the significance of partial slips and temperature jumps on the heat and mass transfer of a boundary layer nanofluid flowing through a stretched or shrinking surface. Considerable consideration is given to the dynamic properties of the nanofluid process, including Brownian motion and thermophoresis. A similarity transform is introduced to obtain a physical model of nonlinear ordinary differential equations, and the Chebyshev method of collocation is used to numerically analyze the influences of parameters of physical flow such as slip, temperature jump, Brownian motion, thermophoresis, suction (or injection) parameters, and Lewis and Prandtl numbers. The numerical results for temperature and concentration profiles, and heat and mass transfer rates, are graphically represented, and insights into the effects of slips and temperature jumps are revealed. In the case of a stretched sheet, the slip parameter enhances the temperature field and increases the thermal boundary layer thickness as well as the concentration function’s boundary layer thickness. When the slip parameter is raised in the case of the shrinking sheet, the dual solutions for temperature and concentration functions are reduced. For the first solution, both the temperature and concentration functions drop as the slip parameter increases, but for the second solution, both the temperature and concentration functions rise as the slip parameter increases. The discoveries have applications in a number of disciplines, including heat transfer in a solar energy collector. Glass blowing, annealing, and copper wire thinning are just a few of the technical and oilfield applications for the current problem. In high-temperature industrial applications, radiation heat transfer research is critical.